Intrinsic periodicity: the forgotten lesson of quantum mechanics

TL;DR

This paper revisits de Broglie's idea of intrinsic periodicity, proposing a harmonic vibrational model of elementary particles that naturally leads to quantum mechanics and offers a new perspective on interactions through space-time modulations.

Contribution

It introduces a classical cyclic dynamics framework based on space-time periodicities that reproduces quantum mechanics and incorporates interactions via geometrodynamical modulations.

Findings

Classical cyclic dynamics match quantum mechanics.

Interactions modeled as space-time recurrence modulations.

Provides a historical perspective on quantization.

Abstract

Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically "periodic phenomena". However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie "periodic phenomenon" in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantization condition. The resulting classical cyclic dynamics formally match ordinary relativistic Quantum Mechanics in both the canonical and Feynman formulations. Interactions are introduced in a geometrodynamical way, similarly to general relativity, by simply considering that variations of kinematical state can be equivalently described in terms of modulations of space-time recurrences, as known from undulatory mechanics. We present this novel quantization prescription from a historical prospective.